Short Course "Porous Media Free Flow Coupling"

This online short course is organised by SFB 1313 and Dropit of the University of Stuttgart as well as by the InterPore Academy. It will be given by Rainer Helmig (University of Stuttgart) and takes place every Monday from 14 November to 12 December 2022.

General Information

Dates: 14 + 21 +28 November and 5 + 12 December
Time: from 3 to 6 pm CET

Hybrid short course
Room U1.003, University of Stuttgart, Pfaffenwaldring 61, 70569 Stuttgart

This short course is organised by SFB 1313 in collaboration with Dropit and InterPore.

Free for SFB 1313 members

InterPore Student Member: 110€
InterPore Student Non – Member: 140€

InterPore Academic Member: 170€
InterPore Academic Non – Member: 230€

InterPore Industry Member: 260€
InterPore Industry Non – Member: 360€

Coupled systems of free flow adjacent to a porous medium appear ubiquitously in nature and in technical applications. Examples for interface-driven transport and exchange processes include soil evaporation, fuel cell water management or food drying. Understanding the complexity of pore-scale mechanisms is paramount to build efficient and reliable mathematical and numerical models.

Typically, averaged models based on the concept of a representative elementary volume (REV) approach are chosen to overcome the enormous computational demand of solving these types of systems on the pore scale. However, this leads to a loss of detailed sub-scale processes which might critically affect the global system behavior.

The aim of the lecture is to give an insight into the physical-mathematical and numerical modelling of coupled free flow and porous-media flow systems. The special challenges of the physical-mathematical modelling will be discussed.  Selected models will be used to illustrate how promising approaches can lead to incorrect results.

Remark: Each topic  will be closed with a summary followed with a discussion. If you have a problem that you want to be discussed, please let us know. I will try to discuss them with you at the end of each lecture and find solutions.

First day (3 hours)


  • What are the most important fields of application (from salt precipitation to fuel cells and bio-technology)?
  • What are the main challenges for modelling coupled porous media-free flow systems interfaces on different scales?

Model concepts:

  • Free-flow system
    • Laminar and turbulent flow
    • Boundary layer effects

Second day (3 hours)

Model concepts:

  • Porous-media system I (Pore-scale)
  • Porous-media system II (Darcy-scale)

Coupling concept for mass, momentum and energy transfer:

  • Coupling: porous media (Pore scale) - free flow

From a 3d to a PNM model 

  • Coupling: porous media (REV-scale) - free flow

Darcy (Forchheimer) – Navier-Stokes- coupling

Third day (3 Hours)

Different coupling concepts (pro and cons)

  • How can we integrate interfaces on the different scales?

Introduction to numerical solution strategies

  • Porous media flow (box or FV-methods (cell-centred or MPFA)

Fourth day (3 hours)

Numerical solution strategies

  • Free flow (staggered-grid FV-Method)
  • Porous media flow (box or FV-methods (cell-centred or MPFA)
  • What is the best coupling concept for the different numerical methods?

Fifth day (3 hours)

Discussion of different solution strategies - what are the advantages and disadvantages?


  • Fuel cells modelling: e.g. what is the best water management?
  • Evaporation processes
    • Technical applications
    • Environmental applications
  • Salt precipitation
  • ….

Final remarks

Prof. Dr.-Ing. Rainer Helmig


The short course is given by Prof. Rainer Helmig of the Department of Hydromechanics and Modelling of Hydrosystems, Institute for Modelling Hydraulic and Environmental Systems, University of Stuttgart. His research covers groundwater hydrology, multi-phase flow in porous media, numerical modeling, and the analysis of coupled processes between the unsaturated zone and the atmosphere. Special focus is on coupling hydrosystem compartments and complex flow and transport processes, as well as integrating data and models. Emphasis in on fundamental questions about physical and mathematical modeling of multi-phase processes, developing algorithms accounting for fluid phase changes and structural media heterogeneities, thereby forming a basis for various model concepts (e.g. predimensioning decontamination strategies and analyses of energy storage (gas, heat), including their effects on groundwater). Recent research focuses on understanding and modeling mass-and heat-flux processes across the land/atmosphere interface as controlled by dynamic interactions between the atmospheric boundary layer and the land surface.

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